Question

Which situation represents a proportional relationship? The cost of purchasing a case of lemons for 1.75 per pound plus 2.25 for the crate. The cost of purchasing a case of lemons for 1.75 per pound plus 2.25 for the crate. The cost of purchasing apples for 5.00 per box with a delivery charge of 7.00. The cost of purchasing apples for 5.00 per box with a delivery charge of 7.00. The cost of purchasing eggs for 3.40 per dozen with a coupon for 2.50 off the total cost. The cost of purchasing eggs for 3.40 per dozen with a coupon for 2.50 off the total cost. The cost of purchasing pork chops for 4.25 per pound plus a shipping fee of 0.50 per pound.

Which situation represents a proportional relationship?

A) The cost of purchasing a case of lemons for 1.75 per pound plus 2.25 for the crate.
B) The cost of purchasing apples for 5.00 per box with a delivery charge of 7.00.
C) The cost of purchasing eggs for 3.40 per dozen with a coupon for 2.50 off the total cost.
D) The cost of purchasing pork chops for 4.25 per pound plus a shipping fee of 0.50 per pound.

Answer 1

Option D, the cost of purchasing pork chops for 4.25 per pound plus a shipping fee of 0.50 per pound, represents a proportional relationship as the total cost is directly proportional to the pounds purchased.

Step-by-step explanation:

To determine which situation represents a proportional relationship, we need to look at whether the total cost changes proportionately with the quantity purchased. A proportional relationship means that as one quantity increases, the other increases in a constant ratio.

Let's examine each option:

• A) The cost of purchasing a case of lemons includes a fixed charge for the crate (2.25), meaning that no matter how many pounds you buy, you'll always have this additional cost. This makes the relationship non-proportional.
• B) The cost of purchasing apples includes a fixed delivery charge (7.00), making the relationship non-proportional.
• C) The coupon for the eggs (2.50 off) makes the relationship non-proportional, as this is a fixed discount applied to the total.
• D) The cost of purchasing pork chops is proportional because for every pound you buy, you pay a fixed amount for the pork chops (4.25 per pound) plus a fixed amount for shipping (0.50 per pound). This maintains a constant ratio, making it a proportional relationship.

Therefore, option D represents a proportional relationship because the total cost changes at a constant rate depending on the number of pounds of pork chops purchased.